Wojciech P. Hunek

A study on new right/left inverses of nonsquare polynomial matrices

A study on new right/left inverses of nonsquare polynomial matrices This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called τ-inverses, σ-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The applicationoriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum variance control, are exploited, and possible applications in signal transmission/recovery in various types of MIMO channels are indicated.

An application of a new matrix inverse in stabilizing state-space perfect control of nonsquare LTI MIMO systems

In this paper, a new definition of a right inverse of nonsquare parameter matrices is derived from MVC-related inverses of nonsquare polynomial matrices. The new definition is employed in a stabilizing state-space perfect control law for nonsquare LTI MIMO systems. A simulation example shows that the new inverse outperforms the classical minimum-norm right inverse.

A new form of a σ-inverse for nonsquare polynomial matrices

This paper presents a new simple form of a polynomial matrix σ-inverse introduced as a result of research works on minimum variance control (MVC) for LTI MIMO nonsquare systems. A new approach to construction of a σ-inverse of a nonsquare polynomial matrix can result in e.g. pole-free design of MVC, which is provided by specially selected degrees of freedom of the σ-inverse. A simulation example in the Matlab® environment illustrates theoretical achievements of the paper.

An application of polynomial matrix σ-inverse in minimum-energy state-space perfect control of nonsquare LTI MIMO systems

In this paper a concept of application of polynomial matrix σ-inverse in multivariable state-space perfect control is presented. The new inverse is derived from perfect control of systems described by the input-output approach. Rather surprisingly, the σ-inverse clearly outperforms some other inverses of nonsquare parameter matrices, including the classical minimum-norm right one. A minimum-energy simulation example made in Matlab/Simulink confirms the usefulness of the proposed method.

Finite approximations of a discrete-time fractional derivative

This paper presents new results in finite-memory modeling of a discrete-time fractional derivative. The introduced normalized finite fractional derivative is shown to properly approximate its fractional derivative original, in particular in terms of the steady-state properties. A stability analysis is also presented as well as a recursive computation algorithm is offered for finite fractional derivatives.

New SVD-based matrix H-inverse vs. minimum-energy perfect control design for state-space LTI MIMO systems

In this paper a new SVD-based inverse of nonsquare parameter matrices is presented. An intriguing impact of H-inverse on minimum-energy design of perfect control inputs is emphasized. Now, the new inverse corresponds to the polynomial matrix S-inverse introduced by Hunek and Latawiec for systems described in the input-output framework. Note that the new inverse can be extended to cover the polynomial and rational forms, thus giving rise to the introduction of a new class of expected inverses.

New Results in Generalized Minimum Variance Control of Computer Networks

In this paper new results in adaptive (generalized) minimum variance control of packet switching computer networks are presented. New solutions, corresponding to the new inverses of the nonsquare polynomial matrices, can be used for design of robust control of multivariable systems with different number of inputs and outputs. Application of polynomial matrix inverses with arbitrary degrees of freedom creates the possibilities to optimal control of computer networks in terms of usage their maximal bandwidth. Simulation examples made in Matlab environment show big potential of presented approach. DOI: http://dx.doi.org/10.5755/j01.itc.43.3.6268

Adaptive finite fractional difference with a time-varying forgetting factor

Normalized finite fractional differences are considered as an approximation to the Grunwald-Letnikov fractional difference. In particular, adaptive finite fractional difference (AFFD) is recalled and effectively modified by the introduction of a time-varying forgetting factor. The modified AFFD is shown in simulations to provide an excellent approximation performance, both in terms of the modeling accuracy and robustness.

Contribution of a new matrix H-inverse to stabilizing the perfect control for LTI MIMO state-space systems

In this paper an useful application of a new right H-inverse to stabilization of perfect control for LTI MIMO discrete-time systems in state-space is shown. Following the recently introduced H-inverse, its intriguing property giving the stable perfect control is indicated here. Now, the SVD-based H-inverse with parameter and polynomial degrees of freedom clearly outperforms the classical minimum-norm right T-inverse in terms of its contribution to stable perfect control design. Simulation studies performed in Matlab environment confirm the big potential of the proposed method over existing ones.

Constrained minimum variance control of nonsquare LTI MIMO systems

Constrained minimum variance control is offered for nonsquare LTI MIMO systems. A constrained control design takes advantage of the so-called control zeros. The new control strategy is compared with familiar generalized minimum variance control and possible application areas of the two are discussed.